The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  1  1  X  0  1  1  0  0  0  X
 0  1  0  0  0  0  0  0  0  0  0  1  1  1  X  X X+1  X  1  1  1  X
 0  0  1  0  0  0  0  0  X  X  1  X  0  X  1  1 X+1  0  1 X+1  1  X
 0  0  0  1  0  0  X  1 X+1  1  1  1 X+1  X  X X+1 X+1  0 X+1  X  X  0
 0  0  0  0  1  0 X+1  1  0 X+1  X  X  1 X+1  X  0  X  X X+1  1  X  X
 0  0  0  0  0  1  1  X  1  1  0  X  1  0 X+1  X  X X+1 X+1  0  X  X

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+421x^16+196x^18+1210x^20+420x^22+1190x^24+364x^26+236x^28+44x^30+12x^32+2x^36

The gray image is a linear code over GF(2) with n=44, k=12 and d=16.
As d=16 is an upper bound for linear (44,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 79.8 seconds.